90,396

2² × 3⁶ × 31

90,396 has digital root 9. The neighboring primes are 90379 and 90397; its proper-divisor sum differs from the starting integer by 64,040.

Prime Factor Structure

Factorization String 2^2 × 3^6 × 31

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 42

Divisor Sum (σ) 244,832

Proper Divisor Sum 154,436

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #90379 ← → #90397

Radix Representation

Decimal	90396
Binary	10110000100011100 (17 bits)
Octal	0o260434
Hexadecimal	0x1611C

Divisor Catalog (42)

1 2 3 4 6 9 12 18 27 31 36 54 62 81 93 108 124 162 186 243 279 324 372 486 558 729 837 972 1,116 1,458 1,674 2,511 2,916 3,348 5,022 7,533 10,044 15,066 22,599 30,132 45,198 90,396

Collatz Trajectory (63 steps to reach 1)

Iterative sequence n → n/2 (if even) or 3n+1 (if odd):

90,396 45,198 22,599 67,798 33,899 101,698 50,849 152,548 76,274 38,137 114,412 57,206 28,603 85,810 42,905 128,716 64,358 32,179 96,538 48,269 144,808 72,404 36,202 18,101 54,304 27,152 13,576 6,788 3,394 1,697 5,092 2,546 1,273 3,820 1,910 955 2,866 1,433 4,300 2,150 1,075 3,226 1,613 4,840 2,420 1,210 605 1,816 908 454 227 682 341 1,024 512 256 128 64 32 16

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